Question
In ∆ABC , G is the centroid , AB = 8 cm, BC= 10 cm and
AC = 12 cm , find GD, where D is the mid-point of BC?Solution
If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 82 + 122 = 2{AD 2 + (10/2) 2 } or 64 + 144 = 2{AD 2 + 25} or 208/2 = AD 2 + 25 or 104 = AD 2 + 25 or AD 2 = 104 – 25 = 79 or AD = √79 = √79 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 4√13 = 4√13/3cm
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